The Israeli dati-leumi/chardali posek Rav Shomo Aviner answers hundreds of text messages and emails a day, providing "mini-teshuvot" to any kind of question anyone wants to ask. Some of them are published on his website:

In my experience, his assistant usually answers emails (after getting the answer from the Rav) on the same day.

Are there any other rabbis who give quick answers to questions about Jewish law or hashkafa in a similar manner, through email or text?

The only other example I can think of is Chabad's "Ask-the-rabbi" feature, but that is directed randomly to shluchim, rather than to a single rabbi. In addition, in my experience if the question involves the details of Jewish law, the "ask-the-rabbi" rabbi will usually just recommend that I contact my local Chabad rabbi.

Just wondering if there are other rabbis doing anything similar to what R' Aviner does! Thanks for your help.